23.3.34 problem 34

Internal problem ID [5748]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 3. THE DIFFERENTIAL EQUATION IS LINEAR AND OF SECOND ORDER, page 311
Problem number : 34
Date solved : Tuesday, September 30, 2025 at 02:02:28 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (b x +a \right ) y+y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 31

ode:=(b*x+a)*y(x)+diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \operatorname {AiryAi}\left (-\frac {b x +a}{b^{{2}/{3}}}\right )+c_2 \operatorname {AiryBi}\left (-\frac {b x +a}{b^{{2}/{3}}}\right ) \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 42

ode=(a + b*x)*y[x] + D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 \operatorname {AiryAi}\left (-\frac {a+b x}{(-b)^{2/3}}\right )+c_2 \operatorname {AiryBi}\left (-\frac {a+b x}{(-b)^{2/3}}\right ) \end{align*}

✓ Sympy. Time used: 0.046 (sec). Leaf size: 42

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
y = Function("y") 
ode = Eq((a + b*x)*y(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} Ai\left (- \frac {a}{\left (- b\right )^{\frac {2}{3}}} + x \sqrt [3]{- b}\right ) + C_{2} Bi\left (- \frac {a}{\left (- b\right )^{\frac {2}{3}}} + x \sqrt [3]{- b}\right ) \]